Families of nearly ordinary Eisenstein series on unitary groups

Wan, Xin

doi:10.2140/ant.2015.9.1955

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Families of nearly ordinary Eisenstein series on unitary groups

Xin Wan

Appendix: Kai-Wen Lan

Vol. 9 (2015), No. 9, 1955–2054

DOI: 10.2140/ant.2015.9.1955

Abstract

We use the doubling method to construct $p$ -adic $L$ -functions and families of nearly ordinary Klingen Eisenstein series from nearly ordinary cusp forms on unitary groups of signature $(r, s)$ and Hecke characters, and prove the constant terms of these Eisenstein series are divisible by the $p$ -adic $L$ -function, following earlier constructions of Eischen, Harris, Li, Skinner and Urban. We also make preliminary computations for the Fourier–Jacobi coefficients of the Eisenstein series. This provides a framework to do Iwasawa theory for cusp forms on unitary groups.

Keywords

Iwasawa theory, ordinary, Klingen Eisenstein series, unitary groups, $p$-adic $L$-function

Mathematical Subject Classification 2010

Primary: 11R23

Milestones

Received: 12 February 2014

Revised: 27 June 2015

Accepted: 18 August 2015

Published: 4 November 2015

Authors

Xin Wan
Department of Mathematics Columbia University Room 509, MC 4406 2990 Broadway New York, NY 10027 United States

Kai-Wen Lan
School of Mathematics University of Minnesota Minneapolis, MN 55455 USA

Vol. 9, No. 9, 2015